Answer to Question #278913 in Statistics and Probability for Tricia

Question

one sample z test A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 8.2 years. The o if the population is 2.3 years. At a = 0.05, can it be concluded that the average age of the taxis in his company is less than the national average?

Answer 1

Null & alternative hypothesis:

$H_0:\mu=9$

$H_a:\mu<9$

Level of significance and critical value:

significance level $\alpha=0.05$

Critical value = 1.96

Test statistic:

Sample size is 40, so z-test is appropriate.

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{8.2-9}{\frac{2.3}{\sqrt{40}}}=-2.2$

$P(z<-2.2)=0.0139$

Statistical decision:

Hence, p-value is less than alpha (0.0139 < 0.05), so we reject Null Hypothesis.

Conclusion:

It can conclude that the average age of the taxi in the company is less than the national average.